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Linear & Abstract Algebra

- Vector spaces and linear transformations. Groups and other algebraic structures along with Number Theory.
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Jan16-12 Greg Bernhardt
Please post any and all homework or other textbook-style problems in one of the Homework & Coursework Questions...
Feb23-13 09:24 AM
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I want to show that the set of points (p,q) on the plane with rational coordinates p and q is countable. I proved set...
Jun20-09 04:41 PM
2 1,754
hello guys. What does true randomness mean Is it that you cannot predict the next number in the sequence ? Can...
Dec25-10 02:56 AM
2 1,754
\frac{a}{n}=\sqrt{a};a > 0;n>1 How do I prove that a=4, and n=2 is the only solution? I'm pretty sure it is, but I...
Jan2-11 11:04 PM
7 1,754
When I have a matrix like this: 0 0 1 0 0 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 I can get most non zero values in...
Jan21-11 02:07 AM
3 1,754
I do not know if this is a common/standard construction, so here is my motivation for this question. From Crystal...
Jul21-11 09:06 AM
2 1,754
I don't know anything of complex analysis or analytic number theory or analytic continuation. But i read about zeta...
Feb25-12 08:24 AM
2 1,754
it is possible to evaluate sums over the set of Rational so \sum_{q} f(q) with q= \frac{m}{n} and m and n are...
Mar31-12 06:39 PM
A. Bahat
4 1,754
I choose a random number p_1 \in and a subsequent series of (increasingly smaller) random numbers p_i \in . Then I...
Feb10-13 09:59 PM
6 1,754
Suppose that \mathbb Z_n\cong \mathbb Z/(n)=\{a+bi|a,b\in\mathbb Z_n\} My 1st question: Is every prime element in...
Jan8-11 09:59 AM
0 1,753
Hi, all. Unless I am mistaken, I am able to prove that the number G_n(z) of primes, no greater than the n-th prime...
Jan12-11 09:50 PM
0 1,753
I have run into a problem where I have a frieze pattern F, the frieze pattern has horizontal refelctive symmetry,...
Apr18-11 11:29 PM
1 1,753
Suppose I have a matrix that looks like this 2.415212e-09 9.748863e-10 -2.415212e-09...
Apr25-12 03:21 AM
3 1,753
I need to solve the equations of type ax+ay-xy=c (or) a(x+y)-xy=c In this equation a &...
Jul28-05 12:55 AM
10 1,752
I have been working on constructing a method to factor composite numbers composed of two odd prime numbers a and b. As...
Nov21-05 09:37 PM
0 1,752
Given R=all non-zero real numbers. I have a mapping Q: R-> R defined by Q(a) = a^4 for a in R. I have to show that...
Oct26-06 02:52 PM
13 1,752
Does anyone have any ideas on how to even start this problem? I am supposed to find a general solution in rational...
Dec12-06 03:01 AM
2 1,752
This is a question in my textbook: "The hyperplanes H1 and H2 have dimensions p and q, respectively. What is the...
Aug6-08 11:48 AM
5 1,752
Dear All, I have a linear system of equations such as Ax = b where A is a m-by-n matrix and m < n and A is a full...
May26-12 07:52 AM
1 1,752
Is it correct to say that any order 4 group is only isomorphic to either C4 or C2+C2 ? where C4 is the order 4...
May23-12 03:10 PM
3 1,751
Im taking a group theory course at the moment in my third year of a theoretical physics degree. In my textbook the...
Dec15-11 10:56 AM
7 1,750
Hi, I have the following \underset{\|\mathbf{x}\|^2=1}{\text{max...
Mar14-12 02:24 AM
0 1,750
I'm really stuck on the following problem: I'm trying to determine whether or not 5^10^5^10^5 is divisible by...
Feb8-06 01:50 PM
9 1,749
(123)x=a (456)y=b (789)z=c For which values (a,b,c) does the above equation have a solution where a,b,c,x,y,z...
Jun24-07 09:22 AM
1 1,749
I know that all Lie algebras comprised of strictly upper triangular matrices are nilpotent. It would seem that there...
Oct9-07 04:45 AM
matt grime
2 1,749
My definition of a strongly nilpotent element is: Let a be in ring R the element a is strongly nilpotent if for...
Aug30-08 10:14 PM
1 1,749
I read in some text the following: Quaternion algebra becomes a normed vector(linear) space with appropriate norm...
Dec23-06 06:36 PM
2 1,747
Hello all, I have recently encountered a tensor which is said to have the property "zero double trace". I am...
Dec12-08 04:23 AM
4 1,747
"Let p be a prime such that there exists a solution to the congruence x^2\equiv - 2\mod p. THEN there are integers a...
Feb24-10 09:27 PM
robert Ihnot
7 1,747
I saw the following problem on my abstract algebra book (dummit && foote) , I tried to solve it but I couldn't : Let...
Oct11-10 04:03 AM
3 1,747
What does x=pmodn mean where x,p,are integers and n is a natural number?
Mar6-04 04:50 PM
2 1,746
Since the the discovery of the complex number field resulted in part from efforts to resolve the quadratic formula...
Mar6-08 09:37 AM
3 1,746
I have a question that I am trying to find proof and/or references for: Suppose we have two sets of points (P1 and...
Jan10-09 01:17 PM
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My best guess is this fits in algebra, I've been scratching my head with this for a while. I have a three...
Apr11-10 01:53 PM
3 1,746
sorry im new and posted instead of currently writing the post
May16-11 09:26 AM
2 1,746
I am using the Law of Cosines to extract and angle I need from a shaft that is turning on an air engine by piston...
Jan4-12 10:59 PM
Simon Bridge
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I think i'm lost on a key concept in LA. I was asked a question about what MxN a matrix needed to be in order to...
Feb8-05 07:49 PM
4 1,745
Question: Let G be a group of order p^n > 1 where p is prime. If H is a subgroup of G, show that it is subnormal in G....
Aug2-07 05:04 PM
4 1,745
Hey guys, I need to prove a few theorems about vector spaces using the axioms. a) Prove: if -v = v, then v = 0 ...
Jan27-08 05:19 PM
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So I'm kind of confused about the definition: a-b\in I Why a - b instead of a + b?
Jan27-08 01:44 PM
3 1,744
Hi, Let's say I have two points: Pa = (0, 0, -30) Pb = (-2.5, -2.5, 7.5) and I want to find the X and Y...
Jan3-09 10:51 AM
8 1,744

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